Using embedding functions with a deep network

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for using embedded function with a deep network. One of the methods includes receiving an input comprising a plurality of features, wherein each of the features is of a different feature type; processing each of the features using a respective embedding function to generate one or more numeric values, wherein each of the embedding functions operates independently of each other embedding function, and wherein each of the embedding functions is used for features of a respective feature type; processing the numeric values using a deep network to generate a first alternative representation of the input, wherein the deep network is a machine learning model composed of a plurality of levels of non-linear operations; and processing the first alternative representation of the input using a logistic regression classifier to predict a label for the input.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. application Ser. No. 13/803,779, filed onMar. 14, 2013, which claims the benefit of priority under 35 U.S.C.§119(e) of U.S. Provisional Application No. 61/666,684, filed on Jun.29, 2012. The disclosures of the prior applications are considered partof and are incorporated by reference in the disclosure of thisapplication.

BACKGROUND

This specification relates to machine learning models.

Machine learning models receive input and generate an output based onthe received input and on values of the parameters of the model.Generally, a given machine learning model may be composed of, e.g., asingle level of linear or non-linear operations or may be a deepnetwork, i.e., a machine learning model that is composed of multiplelevels of non-linear operations.

SUMMARY

In general, one innovative aspect of the subject matter described inthis specification can be embodied in methods that include the actionsof receiving an input comprising a plurality of features, wherein eachof the features is of a different feature type; processing each of thefeatures using a respective embedding function to generate one or morerespective floating point vectors, wherein each of the embeddingfunctions operates independently of each of the other embeddingfunctions, and wherein each of the embedding functions is used forfeatures of a respective feature type; processing the floating pointvectors using a deep network to generate a first alternativerepresentation of the input, wherein the deep network is a machinelearning model composed of a plurality of levels of non-linearoperations; and processing the first alternative representation of theinput using a logistic regression classifier to predict a label for theinput. Other embodiments of this aspect include corresponding computersystems, apparatus, and computer programs recorded on one or morecomputer storage devices, each configured to perform the actions of themethods.

A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of them installed on the system that inoperation causes or cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions.

The foregoing and other embodiments can each optionally include one ormore of the following features, alone or in combination. The method canfurther include: processing the plurality of features using a primarymachine learning model to generate a second alternative representationof the input; and processing the second alternative representation ofthe input along with the first alternative representation of the inputusing the logistic regression classifier to predict the label for theinput.

Each of the features includes one or more tokens. Each of the featuresis a sparse feature. At least one of the embedding functions is a simpleembedding function that maps a single token to a floating point vector.At least one of the embedding functions is a parallel embedding functionthat maps each token in a list of tokens to a respective floating pointvector and outputs a single vector that is a concatenation of therespective floating point vectors. At least one of the embeddingfunctions is a combining embedding function that maps each token in alist of tokens to a respective floating point vector and outputs asingle merged vector that is a combination of the respective floatingpoint vectors. The merged vector is an output of a predetermined linearor nonlinear function of the respective floating point vectors. At leastone of the embedding functions is a mixed embedding function that mapseach token in a list of tokens to a respective floating point vector,generates an initial vector that is a concatenation of the respectivefloating point vectors, merges the respective floating point vectorsinto a merged vector, and concatenates the merged vector with theinitial vector to generate a final vector.

In general, another innovative aspect of the subject matter described inthis specification can be embodied in methods that include the actionsof specifying initial values for parameters of a logistic regressionclassifier, wherein the logistic regression classifier receives a firstalternative representation of an input from a deep learning system and asecond alternative representation of the input from a primary machinelearning model and predicts a label for the input, comprising: settingthe initial value of a first parameter of the classifier that defines aweight assigned by the classifier to second alternative representationsgenerated by the primary machine learning model equal to one and settingthe initial value of a second parameter of the classifier that definesweights assigned by the classifier to first alternative representationsgenerated by the deep learning network equal to zero; and initiating atraining process for the logistic regression classifier based on theinitial values and a set of training data, wherein the values of thefirst and second parameters of the logistic regression classifier areadjusted as part of the training process. Other embodiments of thisaspect include corresponding computer systems, apparatus, and computerprograms recorded on one or more computer storage devices, eachconfigured to perform the actions of the methods.

A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of them installed on the system that inoperation causes or cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions.

The foregoing and other embodiments can each optionally include one ormore of the following features, alone or in combination. During thetraining process, values of parameters of the deep learning system areadjusted using a backpropagation method. The deep learning systemincludes a plurality of embedding functions and each of the plurality ofembedding functions has a respective set of parameters. The deeplearning system includes a deep network having a set of parameters.

Particular embodiments of the subject matter described in thisspecification can be implemented so as to realize one or more of thefollowing advantages. A deep network can be effectively used to predicta label for an input that includes sparse, categorically distinctfeatures. For example, the deep network can be used to effectivelypredict whether a user will select an online advertisement. A deepnetwork can be effectively used in combination with an existing machinelearning model to predict the label for the input. In particular, a deepnetwork can be trained to improve upon the performance of the existingmachine learning model in predicting labels for inputs.

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example deep learning system.

FIG. 2 is a flow diagram of an example process for generating a labeledinput.

FIG. 3 is a block diagram of an example machine learning system.

FIG. 4 is a flow diagram of an example process for training a machinelearning system that includes a primary machine learning model.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of an example deep learning system 100. Thedeep learning system 100 is an example of a system implemented ascomputer programs on one or more computers in one or more locations, inwhich the systems, components, and techniques described below can beimplemented.

The deep learning system 100 receives an input and generates a predictedoutput based on the received input. The input includes a set offeatures, with each feature being of a respective categorically distinctfeature type. A feature of a particular type is a list of active featureelements, i.e., a list of tokens or of token-value pairs, selected froma vocabulary of possible active feature elements of the feature type.For example, the tokens may be words in a natural language, e.g.,English, and the vocabulary for the feature type may be the known wordsin the natural language. The vocabularies for the feature types may beoverlapping or non-overlapping and the list for a given feature type maybe ordered or unordered. Generally, each of the features is a sparsefeature. A feature of a given type is sparse if it has a high likelihoodof containing only a small subset of the possible tokens for that type.For example, if features of a particular feature type can potentiallyinclude any English word, a given feature will include only a very smallsubset of the possible values for that feature type, i.e., only oneEnglish word out of the entire set of English words.

For example, the deep learning system can receive a respective featureof an input A 104 from each of a set of feature type data stores 102.Each of the feature type data stores 102 stores a feature of input A 104that is of a distinct type. For example, the input A 104 can identify aparticular online advertisement presentation setting, and each of thefeatures of the input can be a property of a distinct type of theadvertisement presentation setting. For example, one of the features canbe some or all of the words in the advertisement creative, another ofthe features can be some or all of the words in a search query submittedto a search engine by a user in response to which the advertisement maypotentially be displayed, another of the features can be the country oforigin of the search query, and so on.

The deep learning system 100 uses the received input features to predicta label for the input, e.g., to be stored in a labeled input data store112, or to be used for some immediate purpose. In particular, thelabeled input can be a predicted value for one or more binary variables.In the online advertising context, for example, where the input featuresare features of an online advertisement presentation setting, the deeplearning system 100 can generate a prediction for whether or not a userwill select, e.g., submit an input selecting, the advertisement if it ispresented to the user. A user selection may be, e.g., a “click” on theadvertisement with an input device, a touch input selecting theadvertisement on a touchscreen device, or a selection made using anyother suitable selection mechanism.

The machine learning system 100 includes a set of embedding functions106, a deep network 108, and a logistic regression classifier 110. Insome implementations, the embedding functions 106 are included in thedeep network 108. Each of the embedding functions 106 receives arespective feature of a respective type and, in accordance with a set ofparameters, applies a transformation to the feature that maps thefeature into a numeric representation. For example the numericrepresentations can be one or more floating point values or one or morequantized integer values whose encoding represents floating pointvalues. Embedding functions will be described in more detail below withreference to FIG. 2.

The deep network 108 is a machine learning model that is composed ofmultiple levels of non-linear operations, with each level having arespective set of parameters. That is, the deep network 108 receives asan input the floating point representations of the input featuresgenerated by the embedding functions and applies one or more non-lineartransformations to the floating point representations to generate analternative representation of the input. For example, the deep network108 may include one or more neural network layers that perform arespective nonlinear transformation on its input, a sparse binary outputlayer, or both. The logistic regression classifier 110 receives thealternative representation generated by the machine learning model andpredicts the label for the input, i.e., determines the value of one ormore binary values in accordance with values of parameters of theclassifier.

FIG. 2 is a flow diagram of an example process 200 for determining alabel for a particular input. For convenience, the process 200 will bedescribed as being performed by a system of one or more computerslocated in one or more locations. For example, a deep learning system,e.g., the deep learning system 100 of FIG. 1, appropriately programmed,can perform the process 200.

The system obtains features of an input (step 202). As described above,each of the features is of a different type and is either an ordered orunordered list of tokens or token-value pairs.

The system processes each feature using the embedded function for thefeature type of the feature (step 204) to generate a floating-pointvector representation of the feature. Depending on the feature type andon the implementation, the embedding function for a given feature typecan be any of a variety of embedding functions.

For example, for a feature type whose features consist of a singletoken, the embedding function may be a simple embedding function. Asimple embedding function maps a single token to a floating pointvector, i.e., a vector of floating point values. For example, the simpleembedding function may map a token “cat” to a vector [0.1, 0.5, 0.2] andthe word “iPod” to a vector [0.3, 0.9, 0.0], based on current parametervalues, e.g., using a particular lookup table.

As another example, for a feature type whose features can potentiallyconsist of a list of two or more tokens, the embedding function may be aparallel embedding function. A parallel embedding function maps eachtoken in a list of tokens to a respective floating point vector andoutputs a single vector that is the concatenation of the respectivefloating point vectors. For example, for an ordered list of tokens{“Atlanta”, “Hotel”}, the parallel embedding function may map “Atlanta”to a vector [0.1, 0.2, 0.3] and “Hotel” to [0.4, 0.5, 0.6], and thenoutput [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]. In order to identify therespective floating point vectors, the parallel embedding function mayuse a single lookup table or multiple different look up tables.

As another example, for a feature type whose features can potentiallyconsist of a list of two or more tokens, the embedding function may be acombining embedding function. A combining embedding function maps eachtoken in the list to a respective floating point vector and then mergesthe respective floating point vectors into a single merged vector. Thecombining embedding function can merge the respective floating pointvector using a linear function, e.g., a sum, average, or weighted linearcombination of the respective floating point vectors, or using anonlinear function, e.g., a component-wise maximum or a norm-constrainedlinear combination, for example. In order to identify the respectivefloating point vectors, the parallel embedding function may use a singlelook up table or multiple different look up tables. For example, for theordered list {“Atlanta”, “Hotel”}, the parallel embedding function maymap “Atlanta” to a vector [0.1, 0.2, 0.3] and “Hotel” to [0.4, 0.5,0.6], and then output the sum of the two vectors, i.e., [0.5, 0.7, 0.9].

As another example, for a feature type whose features can potentiallyconsist of a list of two or more tokens, the embedding function may be amixed embedding function. A mixed embedding function maps each token ina list of tokens to a respective floating point vector and generates aninitial vector that is the concatenation of the respective floatingpoint vectors. The mixed embedding function then merges the respectivefloating point vectors into a merged vector and concatenates the mergedvector with the initial vector. For example, for the ordered list{“Atlanta”, “Hotel”}, the mixed embedding function may output aconcatenation of the vectors output by the parallel embedding functionand the combining embedded function, i.e., [0.1, 0.2, 0.3, 0.4, 0.5,0.6, 0.5, 0.7, 0.9].

Depending on the implementation, the system may utilize two differentkinds of embedding functions for two different feature types, and thetwo embedding functions may or may not share parameters. For example,the system may utilize a combining embedding function for a firstfeature type and a mixed embedding function for a second feature type.

If one or more of the features are not discrete, prior to processing thefeature using an embedding function, the system uses a hashing functionto hash each non-discrete feature. The system can then partition eachhashed feature into one of a pre-determined set of partitions, andprocess a value corresponding to the partition using the embeddingfunction for the feature. Additionally, if a particular feature cannotbe obtained, the system can map that feature to a pre-determined value.

In some implementations, instead of floating point values, a givenembedding function may generate a different kind of numeric values. Forexample, the embedding function may generate quantized integer valueswhose encoding represents floating point values.

The system processes the floating-point vector representations using adeep network (step 206). The deep network can be, e.g., the deep network108 of FIG. 1. The deep network includes multiple layers of non-lineartransformations, with each transformation being defined based on valuesof a respective set of parameters. For example, the deep network caninclude one or more hidden neural network layers and a sparse binaryoutput layer, e.g., a layer that outputs a vector that is 0 or 1 atevery position. In general, the deep network generates an alternativerepresentation of the input based on the floating-point vectorrepresentations of the features of the input.

The system processes the alternative representation of the input using alogistic regression classifier (step 208) to predict a label for theinput. The logistic regression classifier predicts the input based onvalues of a set of parameters and the alternative representation. Thelabel for the input is a prediction of the values of one or more binaryvariables, e.g., whether a user will select a given presentation of agiven advertisement.

The process 200 can be performed to determine a label for an input forwhich the desired label is not known. The process 200 can also beperformed on inputs in a set of training data, i.e., a set of inputs forwhich the label that should be predicted by the label is known, in orderto train the system, i.e., to determine optimal values for theparameters of the logistic regression classifier, the deep network, andeach of the embedding functions. For example, the process 200 can beperformed repeatedly on inputs selected from a set of training data aspart of a backpropagation training technique that determines optimalvalues for each of the parameters.

In some implementations, the deep learning system also includes aprimary machine learning model. The primary machine learning model is adifferent machine learning model that has been trained to receive inputfeatures and generate an alternative representation of the input. Insome implementations, the primary machine learning model does notinclude a deep network, i.e., is composed of only a single layer oflinear computations.

FIG. 3 is a block diagram of an example machine learning system 300. Theexample machine learning system 300 includes a deep learning system 302and a primary machine learning model 304. The deep learning system 302includes a set of embedding functions, e.g., the embedding functions 106of FIG. 1, a deep network, e.g., the deep network 108 of FIG. 1, andoptionally a classifier, e.g., a logistic regression classifier, e.g.,the logistic regression classifier 110 of FIG. 1. Each of the deeplearning system 302 and the primary machine learning model 304 receivesa set of features of an input, e.g., from feature type data stores 306,and generates an alternative representation of the input. Thealternative representations of the input are then provided to thelogistic regression classifier 308, which predicts a label for the inputbased on the outputs of the deep learning system 302 and the primarymachine learning model 304. The labeled input can be stored in a labeledinput data store 310 for later use or used immediately.

The classifier 308 predicts the labels based in part on values of a setof parameters. The set of parameters include, for both the deep learningsystem 302 and the primary machine learning model 304, at least onerespective parameter that defines weights that are applied to outputsreceived by the classifier from each. In implementations where one ormore of the deep learning system 302 and the primary machine learningmodel 304 output predicted probabilities for the binary label values,the logistic regression classifier may operate on the log-oddstransformed representations of the binary label values.

In some implementations, the logistic regression classifier 308 and thedeep learning system 302 can be trained in order to improve upon theperformance of the primary machine learning model 304, i.e., in orderfor the machine learning system 300 to predict more frequently a labelfor an input that matches the desired label for the input than would amachine learning system that did not include the deep learning system302.

FIG. 4 is a block diagram of an example process 400 for training amachine learning system that includes a primary machine learning model.For convenience, the process 400 will be described as being performed bya system of one or more computers located in one or more locations. Forexample, a machine learning system, e.g., the machine learning system300 of FIG. 3, appropriately programmed, can perform the process 400.

The system specifies initial values for the parameters of a logisticregression classifier (step 402). In particular, the system assigns avalue for the parameter that corresponds to the weight assigned to theoutput of a primary machine learning model, e.g., the primary machinelearning model 304 of FIG. 3, to one, and the values of the one or moreparameters that correspond to the weight assigned to the output of adeep network, e.g., the deep learning system 302 of FIG. 3, to zero.That is, the initial values are specified such that initially the labelassigned by the classifier will depend only on the output of the primarymachine learning model and not on the output of the deep network.

The system performs a training process to train the logistic regressionclassifier (step 404) using the specified initial values for theparameters and a set of training data. The set of training data includesa set of inputs, each having a respective set of input features, and foreach input a label that should be predicted by the system. Additionally,the training process uses the method of backpropagation to adjust theparameters of all the components of a deep learning network thatprovides input to the logistic regression classifier in a direction thatreduces expected error on the current training example. The deeplearning network includes a deep network, e.g., the deep network 108 ofFIG. 1, and a set of embedding functions, e.g., the embedding functions106 of FIG. 1.

As part of the training process, if the label predicted by the logisticregression classifier for a particular input in the set of training datais different from the known desired label for that particular input, thelogistic regression classifier will adjust its parameters so as toreduce the expected error on that particular input using conventionalgradient based methods. Furthermore, through the method ofbackpropagation, the logistic regression classifier sends an errorsignal to the deep learning network, which allows it to adjust theparameters of its internal components, e.g., the deep network and theset of embedding functions though successive stages of backpropagation.

At the completion of the training process, the system obtains values ofthe parameters of the logistic regression classifier and the deeplearning system (step 406) that have been adjusted during the trainingprocess to improve performance relative to the performance of theprimary machine learning model.

While the above description describes implementations where the outputof the deep learning system and the output of the primary machinelearning model are both used as inputs into a logistic regressionclassifier, the output of the deep learning system can also be used asan input into the primary machine learning model. That is, the output ofthe deep learning system for a given input may be treated as anadditional feature of the input and provided as an input feature to theprimary machine learning model in addition to or instead of the existingfeatures of the input. Alternatively or in addition, one or more of therepresentations of the input that are generated by the variouscomponents of the deep learning system can be used as an input into theprimary machine learning model.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non transitory program carrier for execution by, or to controlthe operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on an artificiallygenerated propagated signal, e.g., a machine-generated electrical,optical, or electromagnetic signal, that is generated to encodeinformation for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them.

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, or multiple processors or computers.The apparatus can include special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application specificintegrated circuit). The apparatus can also include, in addition tohardware, code that creates an execution environment for the computerprogram in question, e.g., code that constitutes processor firmware, aprotocol stack, a database management system, an operating system, or acombination of one or more of them.

A computer program (which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code) can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Computers suitable for the execution of a computer program include, byway of example, can be based on general or special purposemicroprocessors or both, or any other kind of central processing unit.Generally, a central processing unit will receive instructions and datafrom a read only memory or a random access memory or both. The essentialelements of a computer are a central processing unit for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few. Computer readablemedia suitable for storing computer program instructions and datainclude all forms of non-volatile memory, media and memory devices,including by way of example semiconductor memory devices, e.g., EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto optical disks; and CD ROM and DVD-ROMdisks. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's client device in response to requests received from the webbrowser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back end, middleware, or front end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is:
 1. A method performed by one or more computers, themethod comprising: receiving an input comprising a plurality of sparsefeatures, wherein each of the sparse features is of a different featuretype; generating a numeric representation of the input, comprisingprocessing each of the sparse features using a respective embeddingfunction to generate one or more respective numeric values, wherein eachof the embedding functions operates independently of each of the otherembedding functions, and wherein each of the embedding functions isspecific to features of a respective feature type; and providing thenumeric representation of the input as input to a deep networkcomprising a plurality of neural network layers for classification ofthe input.
 2. The method of claim 1, wherein each of the featurescomprises one or more tokens.
 3. The method of claim 1, wherein at leastone of the embedding functions is a simple embedding function that mapsa single token to a floating point vector.
 4. The method of claim 1,wherein at least one of the embedding functions is a parallel embeddingfunction that maps each token in a list of tokens to a respectivefloating point vector and outputs a single vector that is aconcatenation of the respective numeric values.
 5. The method of claim1, wherein at least one of the embedding functions is a combiningembedding function that maps each token in a list of tokens to arespective floating point vector and outputs a single merged vector thatis a combination of the respective numeric values.
 6. The method ofclaim 5, wherein the merged vector is an output of a predeterminedlinear or nonlinear function of the respective numeric values.
 7. Themethod of claim 1, wherein at least one of the embedding functions is amixed embedding function that maps each token in a list of tokens to arespective floating point vector, generates an initial vector that is aconcatenation of the respective numeric values, merges the respectivenumeric values into a merged vector, and concatenates the merged vectorwith the initial vector to generate a final vector.
 8. The method ofclaim 1, wherein the input is a plurality of features of a presentationsetting for an online advertisement and the deep network is configuredto generate an output that represents a predicted likelihood that a userwill select the online advertisement.
 9. A system comprising one or morecomputers and one or more storage devices storing instructions that whenexecuted by the one or more computers cause the one or more computers toperform operations comprising: receiving an input comprising a pluralityof sparse features, wherein each of the sparse features is of adifferent feature type; generating a numeric representation of theinput, comprising processing each of the sparse features using arespective embedding function to generate one or more respective numericvalues, wherein each of the embedding functions operates independentlyof each of the other embedding functions, and wherein each of theembedding functions is specific to features of a respective featuretype; and providing the numeric representation of the input as input toa deep network comprising a plurality of neural network layers forclassification of the input.
 10. The system of claim 9, wherein each ofthe features comprises one or more tokens.
 11. The system of claim 9,wherein at least one of the embedding functions is a simple embeddingfunction that maps a single token to a floating point vector.
 12. Thesystem of claim 9, wherein at least one of the embedding functions is aparallel embedding function that maps each token in a list of tokens toa respective floating point vector and outputs a single vector that is aconcatenation of the respective numeric values.
 13. The system of claim9, wherein at least one of the embedding functions is a combiningembedding function that maps each token in a list of tokens to arespective floating point vector and outputs a single merged vector thatis a combination of the respective numeric values.
 14. The system ofclaim 13, wherein the merged vector is an output of a predeterminedlinear or nonlinear function of the respective numeric values.
 15. Thesystem of claim 9, wherein at least one of the embedding functions is amixed embedding function that maps each token in a list of tokens to arespective floating point vector, generates an initial vector that is aconcatenation of the respective numeric values, merges the respectivenumeric values into a merged vector, and concatenates the merged vectorwith the initial vector to generate a final vector.
 16. The system ofclaim 9, wherein the input is a plurality of features of a presentationsetting for an online advertisement and the deep network is configuredto generate an output that represents a predicted likelihood that a userwill select the online advertisement.
 17. One or more non-transitorycomputer storage media storing instructions that when executed by one ormore computers cause the one or more computers to perform operationscomprising: receiving an input comprising a plurality of sparsefeatures, wherein each of the sparse features is of a different featuretype; generating a numeric representation of the input, comprisingprocessing each of the sparse features using a respective embeddingfunction to generate one or more respective numeric values, wherein eachof the embedding functions operates independently of each of the otherembedding functions, and wherein each of the embedding functions isspecific to features of a respective feature type; and providing thenumeric representation of the input as input to a deep networkcomprising a plurality of neural network layers for classification ofthe input.
 18. The computer storage media of claim 17, wherein at leastone of the embedding functions is a simple embedding function that mapsa single token to a floating point vector.
 19. The computer storagemedia of claim 17, wherein at least one of the embedding functions is aparallel embedding function that maps each token in a list of tokens toa respective floating point vector and outputs a single vector that is aconcatenation of the respective numeric values.
 20. The computer storagemedia of claim 17, wherein at least one of the embedding functions is acombining embedding function that maps each token in a list of tokens toa respective floating point vector and outputs a single merged vectorthat is a combination of the respective numeric values.